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Non-invasive foetal electrocardiography (NI-FECG) has become an important prenatal monitoring method in the hospital. However, due to its susceptibility to non-stationary noise sources and lack of robust extraction methods, the capture of high-quality NI-FECG remains a challenge. Recording waveforms of sufficient quality for clinical use typically requires human visual inspection of each recording. A Signal Quality Index (SQI) can help to automate this task but, contrary to adult ECG, work on SQIs for NI-FECG is sparse. In this paper, a multi-channel signal quality classifier for NI-FECG waveforms is presented. The model can be used during the capture of NI-FECG to assist technicians to record high-quality waveforms, which is currently a labour-intensive task. A Convolutional Neural Network (CNN) is trained to distinguish between NI-FECG segments of high and low quality. NI-FECG recordings with one maternal channel and three abdominal channels were collected from 100 subjects during a routine hospital screening (102.6 min of data). The model achieves an average 10-fold cross-validated AUC of 0.95 ± 0.02. The results show that the model can reliably assess the FECG signal quality on our dataset. The proposed model can improve the automated capture and analysis of NI-FECG as well as reduce technician labour time.